Method for determining lumen penetration of a vapor phase sterilant

ABSTRACT

Concentration of a chemical vapor sterilant, especially, hydrogen perioxide, can be calculated at a point within a lumen based upon physical characteristics of the lumen and process parameters of a sterilization process employing the sterilant.

BACKGROUND

The present invention relates to vapor phase sterilization, and moreparticularly to determining the penetration of vapor phase chemicalsterilants into a lumen.

Presently, vapor phase chemical sterilization is a popular option formedical devices which are temperature sensitive. Vapor phasesterilization encompasses such sterilants as hydrogen peroxide,peracetic acid, ethylene oxide and chlorine dioxide. The chemical vapordiffuses into contact with and sterilizes the surface of the instrument.Penetration of long narrow lumens with the vapor represents one of thelargest challenges. Determination of whether such penetration has beensuccessful is a further challenge. Presently, it remains difficult toplace a reliable sensor in a long narrow lumen. Such sensors aretypically too large to be accommodated within the lumen and theirpresence may disturb the diffusion into the lumen.

Although, directly measuring concentration of a vapor sterilant insidethe lumen remains a challenge, several methods have been put forward fordirectly measuring such concentration within a sterilization chamber ofsuch a sterilization system. For instance, hydrogen peroxideconcentration can be measured by passing lightwaves of certainfrequencies through the chamber and detecting the absorption of thelightwaves to determine the makeup of the gases within the chamber. Inanother method, a thermocouple coated with a catalyst for breaking downhydrogen peroxide can be placed within the chamber and the degree ofheating caused on the thermocouple by the breakdown of hydrogen peroxidecan be used to indicate the concentration of hydrogen peroxide withinthe chamber. Of course, other methods may also be employed to measurethe concentration of hydrogen peroxide or other chemical vapors within asterilization chamber. However, such measurements do not reveal theconcentration within a lumen of a device within a chamber.

The present invention overcomes this and other limitations in the priorart and provides a method for determining the concentration of achemical vapor sterilant within a lumen of a device within asterilization chamber.

SUMMARY OF THE INVENTION

A method according to the present invention assesses a sterilization ofa lumen of a device in a vapor phase hydrogen peroxide sterilizationprocess. The method comprises the steps of: a) measuring concentrationof hydrogen peroxide vapor exterior of the lumen; b) calculating atleast once a concentration of hydrogen peroxide at a selected locationwithin the lumen based upon time of exposure, concentration of hydrogenperoxide exterior of the lumen and the physical characteristics of thelumen; and c) indicating a parameter relevant to said sterilization ofsaid lumen based upon said concentration of said hydrogen peroxide atthe selected location.

The step of indicating can comprise displaying to a user the parameterrelevant to the sterilization of the lumen. Such parameter can compriseconcentration of said hydrogen peroxide at the selected location. Stepsa) and b) can be repeated multiple times to calculate an integratedvalue of the concentration of hydrogen peroxide at the selected locationover a time of exposure and the parameter relevant to the sterilizationof the lumen could comprises such integrated value. The parameterrelevant to the sterilization of the lumen could be a success or failureof the sterilization of the lumen.

The process parameters used in the calculating step preferably comprise:pressure exterior of the lumen, the concentration of peroxide exteriorof the lumen and time. The physical characteristics of the lumen used inthe calculating step preferably comprise: diameter of the lumen, lengthof the lumen to the selected location, type of material forming thelumen and temperature of the material forming the lumen.

Preferably, the calculating step employs a mathematical model in whichthe lumen is assumed to have a single dimension. The calculating stepcan employs a mathematical model solved by iteration.

Preferably the concentration of hydrogen peroxide at the selectedlocation is calculated based upon the following relationship:

${\left. \left. {C_{p} = {C_{o} + {\left( {4k\;{c_{o}/\pi}} \right)\left\{ {\sum\limits^{\;}{\left\lbrack {\sin\left( {n\;\pi\;{x/L}} \right)} \right){\left( {\left( {\exp\left( {t\left( {k - {D\left( {n\;{\pi/L}} \right)}^{2}} \right)} \right)} \right) - 1} \right)/{n\left( {k - {D\left( {n\;{\pi/L}} \right)}^{2}} \right)}}}} \right)}}} \right\rbrack \right\} - {\left( {4c_{o}{\exp({kt})}} \right){\left\{ {\sum\left\lbrack {\left( {\sin\left( {n\;\pi\;{x/L}} \right)} \right)\left( {\exp\left( {- {{Dt}\left( {n\;{\pi/L}} \right)}^{2}} \right)} \right)} \right\rbrack} \right\}/\pi}}};$

where:

-   -   c_(p) represents the concentration of hydrogen peroxide at the        selected location;    -   c_(o) represents the concentration exterior of the lumen;    -   k represents a rate constant for losses of hydrogen peroxide;    -   L represents the length of the lumen;    -   D represents the diffusion coefficient for hydrogen peroxide        vapor;    -   x represents the distance into the lumen to the selected        location from exterior of the lumen    -   n represents odd integer counters 1, 3, 5, . . . ; and    -   t represents the time from when hydrogen peroxide vapor first is        introduced exterior of the lumen.

Preferably, k is determined at least in part based upon a materialforming the lumen, the diameter of the lumen and the temperature of thematerial forming the lumen.

In one aspect of the invention, a method is provided for controllingsterilization of a lumen of a device in a vapor phase hydrogen peroxidesterilization process, the method comprising the steps of: measuring aconcentration of hydrogen peroxide vapor exterior of the lumen;calculating at least once a concentration of hydrogen peroxide at aselected location within the lumen based upon process parameters of thesterilization process and physical characteristics of the lumen, whereinthe process parameters include the concentration of hydrogen peroxideexterior of the lumen; and adjusting a parameter of the sterilizationprocess based upon the at least one calculated concentration of hydrogenperoxide at the selected location.

The step of adjusting a parameter of the sterilization process cancomprise adjusting a time of exposure of the device to the vapor phasehydrogen peroxide and/or adjusting the concentration of the hydrogenperoxide exterior of the lumen. The method can comprise repeatedlymeasuring the concentration of hydrogen peroxide exterior of the lumenand calculating the concentration of hydrogen peroxide at the selectedlocation and modifying a parameter of the sterilization process uponachieving a preselected value of hydrogen peroxide at the selectedlocation, such as for instance achieving a preselected value of theintegrated time and concentration exposure at the selected location.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a block diagram of a sterilization system upon which themethod of the present invention can be practiced.

DETAILED DESCRIPTION

FIG. 1 represents, in block diagram form, a sterilizer 10 comprising achamber 12, a vacuum pump 14 for drawing a vacuum upon the chamber 12and an injector 16 for injecting a steriliant, namely hydrogen peroxide,into the chamber 12. A medical device 18 having a lumen 20 is disposedwithin the chamber 12 for sterilization. A hydrogen peroxide sensor 22,temperature sensor 24 and pressure sensor read hydrogen peroxideconcentration, and the temperature and pressure within the chamber 12and provide their output to a control system 26 comprising a CPU 28 anddisplay 30.

In its basic form, the sterilizer 10 operates by drawing a vacuum uponthe chamber 12 via the pump 14 and injecting hydrogen peroxide into thechamber 12 with the injector 16. The hydrogen peroxide may enter thechamber in either vapor or liquid form, with any liquid hydrogenperoxide vaporizing upon entry into the low pressure environment of thechamber 12. Contact with the hydrogen peroxide vapor sterilizes thedevice 18.

To sterilize the lumen 20 hydrogen peroxide vapor must diffuse therein.The hydrogen peroxide sensor 22 can measure the concentration ofhydrogen peroxide within the chamber 12 but cannot directly measure theconcentration of hydrogen peroxide achieved within the lumen 20,especially at a difficult to penetrate midpoint 32 of the lumen 20. Toovercome this limitation, the present invention provides a method forcalculating the concentration of hydrogen peroxide achieved at aspecific location, such as the midpoint 32, within the lumen 20 basedupon parameters of the sterilization cycle and the physical parametersof the medical device 18.

The mathematical model of the present invention is based upon a massbalance for hydrogen peroxide at a point inside a masstransport-restricted region of the load, such as the center of a lumen32. The mass balance around a lumen is in the form of a differentialequation, an initial condition and a boundary condition:∂c _(p) /∂t=D∇ ² c _(p) +kc _(p)

Initial condition: t=0, c_(p)=0 everywhere

Boundary condition: c_(p)=c_(o) at the two ends of the lumen

c_(p)=hydrogen peroxide concentration at the point of interest in thelumen, g/cm³

t=time

D=diffusion coefficient, cm²/sec

∇²=differential operator, ∂²/∂x² for one-dimensional diffusion in thex-direction, cm⁻²

k=rate constant for losses in the lumen, sec⁻¹

c_(o)=hydrogen peroxide concentration at the two entrances to the lumen,g/cm³

The differential equation states that:The change of peroxide mass per volume with time=The rate of mass inputper volume by diffusion+The rate of mass input per volume by internalprocesses

On the right side of the equation, the rate of delivery of hydrogenperoxide mass per volume is specified by the diffusion term, which isdriven by the concentration gradient from the chamber 12 to the lumen20. The rate of mass input per volume to the lumen 20 by internalprocesses is a negative term, whenever mass is lost in the lumen 20 bydecomposition, absorption, adsorption and condensation. In that case therate constant k is a negative number.

The initial condition requires that the concentration of hydrogenperoxide is zero in the sterilizer chamber 12 and lumen 20 beforeinjection of hydrogen peroxide.

The boundary condition sets the hydrogen peroxide concentration equal toc_(o) in the chamber 12 at both entrances 34 to the lumen. In practicethis value changes with time during the sterilization cycle, but ananalytical solution may be obtained for the one-dimensional case withconstant external concentration and position-invariant diffusioncoefficient to give a useful calculation of the lumen concentration withtime. The analytical solution to this case is a complicated set of termsand variables, which must be evaluated to solve for the lumenconcentration:

$\left. \left. {C_{p} = {C_{o} + {\left( {4k\;{c_{o}/\pi}} \right)\left\{ {\sum\limits^{\;}{\left\lbrack {\sin\left( {n\;\pi\;{x/L}} \right)} \right){\left( {\left( {\exp\left( {t\left( {k - {D\left( {n\;{\pi/L}} \right)}^{2}} \right)} \right)} \right) - 1} \right)/{n\left( {k - {D\left( {n\;{\pi/L}} \right)}^{2}} \right)}}}} \right)}}} \right\rbrack \right\} - {\left( {4c_{o}{\exp({kt})}} \right){\left\{ {\sum\left\lbrack {\left( {\sin\left( {n\;\pi\;{x/L}} \right)} \right)\left( {\exp\left( {- {{Dt}\left( {n\;{\pi/L}} \right)}^{2}} \right)} \right)} \right\rbrack} \right\}/\pi}}$

This solution assumes that the initial hydrogen peroxide concentrationc_(i) in the chamber 12 and load of devices 18 is c_(p)=0. A moregeneral solution would be obtained by replacing c_(o) with (c_(o)−c_(i))in the second and third terms of the solution equation above to allowfor a non-zero initial hydrogen peroxide concentration.

The hydrogen peroxide concentration in the chamber 12 is measured ateach time point after injection by the peroxide monitor 22. In thesolution equation above, the concentration c_(o) at both lumen entrancesmay be estimated as the hydrogen peroxide concentration in the chamber12, because the resistance to mass transfer is generally small from thebulk region of the chamber 12 to the periphery of the load.

The summation of terms Σ in the solution occurs over the series n=1, 3,5 . . . ∞.

The position of interest, x, in the lumen 20 may be anywhere along theaxis from x=0 cm at one end 34 of the lumen 20 to x=L cm at the otherend. At the center 32 of the lumen 20, which is usually the mostmass-transport restricted region, x/L=0.5.

The solution is evaluated in one-second time points t after injection.

The diffusion coefficient D for hydrogen peroxide is calculated with thepublished correlation (Ref. J. C. Slattery and R. B. Bird, AIChEJournal, 4, 137–142, 1958)D=3.303×10⁻⁴((T+273)^(2.334))/P

Lumen temperature T° C. and chamber pressure P mmHg can be measuredduring the sterilization cycle to evaluate D. As the temperature of thematerial forming the lumen 20 changes only moderately in moststerilization cycles, it can be assumed to be the room temperature atwhich the device 18 was stored prior to the process.

The rate constant k cannot be measured experimentally inside the lumen20 without disturbing the internal environment, so a value is assignedfor each lumen material, such as stainless steel and polyethylene. Thevalue is adjusted to provide an area scale, which correlates efficacyresults from the sterilization cycles, as discussed below.

The concentration at the center 32 of the lumen 20 is calculated fromthe analytical solution equation at each time point during the injectionand diffusion steps of the sterilization cycle with the variables asdefined above. For cycles with a venting step after injection ofhydrogen peroxide, the concentration in the lumen 20 during the firstminute of diffusion is set equal to the chamber concentration, becausehydrogen peroxide is driven by air pressure into the lumen 20.Concentration in the lumen 20 for the remainder of the diffusion step iscalculated by subtracting losses of decomposition, absorption,adsorption and condensation.

Efficacy of the sterilization cycle depends strongly upon theconcentration of hydrogen peroxide in the chamber 12 and in the load.However, other process variables are also important, such as chamber andload temperature, size and composition of the load and exposure time.For a fixed load configuration in a particular sterilizer with aqualified sterilization cycle, temperature remains relatively constantduring injection, so concentration and exposure time become the mostimportant control variables. Area under a concentration-time curve is auseful index for quantifying cycle performance to compare with efficacyas measured via biological indicators.

An estimate of the area under the concentration-time curve is obtainedby summing the one-second concentration values in the injection anddiffusion steps of the cycle, as shown in Table 1 for sterilizationcycles in a STERRAD® 200 hydrogen gas/plasma sterilizer available fromAdvanced Sterilization Products division of Ethicon, Inc., Irvine,Calif., with different lumens in the validation load. The area scale forstainless steel (SS) is established by setting the value of the rateconstant k equal to 0.46 sec⁻¹ to give an area of approximately 100mg-sec/l for the cycles with 3 mm×500 mm stainless steel lumens at 30°C. This set of lumens is chosen as the basis for the stainless steelarea scale, because 3 mm×500 mm stainless steel lumens are at the limitof the presently approved label claims for the STERRAD® 200 Sterilizer,so they represent one measure of a borderline capability for efficacy.

TABLE 1 Results for the STERRAD ® 200 Sterilizer Model for HydrogenPeroxide Concentration in Lumens Diffusion, Venting and ReactionProcesses Mid-Lumen Temp., Injec- Hydrogen Fraction Lumen, ° C. tionPeroxide Conc. Positive mm dia. × (lumen Time, −k, vs. Time Biologicalmm long material) min. sec⁻¹ Area, mg-sec/l Indicators   3 × 400 SS 306.5 0.46 168, 156, 157 0/72   3 × 500 SS 30 6.5 0.46^(a) 101, 93, 910/96   3 × 400 SS 30 2 0.46 106, 104, 108 0/72   3 × 400 SS 30 1 0.4697, 100, 108 4/72   3 × 400 SS 5 6.5 1.41^(c) 53, 50, 50 1/72   1 × 125SS 30 6.5 4.14^(d) 139, 143, 149 0/36 0.8 × 100 SS 30 6.5 6.47^(e) 133,137, 140, 0/48 136 0.8 × 150 SS 30 6.5 6.47 43, 44 2/24   1 × 500 PE 306.5 0.33^(a) 104, 107, 108 0/36   1 × 700 PE 30 6.5 0.33 34 1/12   3 ×1000 PE 30 6.5 0.037^(f) 262, 261, 245 0/36   3 × 1500 PE 30 6.5 0.03799, 102, 97 1/36   3 × 1500 PE 30 20 0.037 179 0/12   3 × 1500 PE 30 250.037 188 0/12   3 × 1500 PE 30 30 0.037 205 0/12 SS—Stainless steelPE—Polyethylene ^(a)k chosen to give 100 mg-sec/l area threshold^(c)k_(5C) calculated from k_(30C), vapor pressure data anddecomposition rate factor ^(d)k calculated as (k_(3 mm)) × 3 surface tovolume ratio × 3 diffusion radius ratio ^(e)k calculated as (k_(3 mm)) ×3.75 surface to volume ratio × 3.75 diffusion radius ratio ^(f)kcalculated as (k_(1 mm))/(3 surface to volume ratio × 3 diffusion radiusratio)

Shorter 3 mm×400 mm stainless steel lumens in Table 1 have the same rateconstant as for 3 mm×500 mm lumens, because the materials and diametersare the same. However, the area is significantly greater for the shorterlumens, because the centers of these lumens are closer to the lumenentrances. When the injection times are reduced to two minutes and oneminute from 6.5 minutes for 3 mm×400 mm stainless steel lumens, theareas drop to approximately 100 mg-sec/l, and positive biologicalindicators begin to appear. A positive biological indicator indicatesthat some test microorganisms have not been killed. If the temperatureof these lumens is reduced from 30° C. to 5° C., the rate constant 0.46sec⁻¹ must be corrected with kinetic and vapor pressure data to reflectthe decreased decomposition rate and the increased condensation rate ofhydrogen peroxide. The area with the corrected rate constant 1.41 sec⁻¹falls below 100 mg-sec/l with a 6.5 minute injection time, andbiological results are in the positive region.

Correcting the rate constant from 0.46 sec⁻¹ at 30° C. to 1.41 sec⁻¹ at5° C. is initiated by writing the rate constant as the sum of thedecomposition rate constant k^(D) and the condensation rate constantk^(C). At 30° C. the two rate constants can be assumed to be comparablein magnitude, because decomposition proceeds slowly near roomtemperature, while condensation is reduced in warm loads. For a rateconstant 0.46 sec⁻¹ at 30° C., each individual rate constant ofdecomposition k^(D) and condensation k^(C) is approximately 0.46/2=0.23sec⁻¹. The rate constant of condensation k^(C) at 5° C. is calculatedfrom the rate constant of condensation k^(C) at 30° C. by adjusting itfor the ratio of the vapor pressures of hydrogen peroxide at the twotemperatures (Hydrogen Peroxide, Schumb et al., Reinhold Pub. Co., N.Y.,1955, p. 226): k^(C) at 5° C.=0.23 sec⁻¹×(2.77 mm Hg at 30° C./0.46 mmHg at 5° C.)=1.38 sec⁻¹. The rate constant of decomposition k^(D) at 5°C. is calculated from the rate constant of decomposition k^(D) at 30° C.and the rate factors for decomposition at 30° C. and 5° C.: k^(D) at 5°C.=0.23 sec⁻¹×(1 rate factor at 5° C./7 rate factor at 30° C.)=0.03sec⁻¹. The rate factors for decomposition of hydrogen peroxide are takenfrom Table 2 (Ref. FMC Technical Data Sheet, p. 10, rate increases 2.2times per every 10° C.). Finally, the rate constant at 5° C. iscalculated as the sum of the rate constants of condensation k^(C) and ofdecomposition k^(D) at 5° C.: k at 5° C.=1.38 sec⁻¹+0.03 sec⁻¹=1.41sec⁻¹.

TABLE 2 Rate Factor for Decomposition of Hydrogen Peroxide as a Functionof Temperature^(a) Rate Factor for Temperature, ° C. Decomposition  5  1 Base Case 15  2.2 25  4.84 35 10.65 45 23.4 ^(a)The decomposition rateincreases by a factor of 2.2 for each 10° C. rise in temperature (Ref.FMC Technical Data Sheet, p. 10)

The solution equation is restricted to a one-dimensional model, sohydrogen peroxide transport in lumens would be treated similarly with 3mm and with smaller diameters. However, experimental results demonstratethat efficacy in 1 mm and smaller diameter lumens can only be achievedin shorter lumen lengths. Therefore, the model needs to be adjusted toreflect the restricted transport in smaller lumens.

The adjustment for diameter is made in Table 1 by correcting the rateconstant 0.46 sec⁻¹ for 3 mm stainless steel lumens to 4.14 sec⁻¹ for 1mm lumens with factors for the surface to volume ratio and diffusionradius ratio. With this rate constant the area for 1 mm×125 mm lumens isgreater than 100 mg-sec/l and the biological results are negative. Therate constant 0.46 sec⁻¹ is similarly corrected to 6.47 sec⁻¹ for 0.8 mmlumens; lumens with 100 mm length have area values greater than 100mg-sec/l and negative biological results, while lumens at 150 mm lengthhave areas lower than 10.0 mg-sec/l and positive biological results.

The correction of the rate constant 0.46 sec⁻¹ for surface to volumeratio is necessary, because 1 mm lumens have greater surface area insidethe lumens for interaction with hydrogen peroxide molecules relative tothe lumen volume, as compared to 3 mm lumens. The larger surface areacontributes to a greater loss of hydrogen peroxide inside the smallerlumen, which is reflected in a greater rate constant.

Surface  to  volume  ratio  correction  factor = (surface/volume)_(1  mm)/(surface/volume)_(3  mm) = (2 π rL/π r²L)_(1  mm)/(2π rL/π r²L)_(3  mm) = (1/r)_(1  mm)/(1/r)_(3  mm) = (r)_(3  mm)/(r)_(1  mm) = 1.5  mm/0.5  mm = 3

where r represents the lumen or diffusion ratio.

In addition to correction for surface to volume ratio, correction of therate constant 0.46 sec⁻¹ for diffusion radius is necessary, becausediffusion to the wall of the smaller lumen is greater than for thelarger one.

Diffusion  radius  ratio  correction  factor = (r)_(3  mm)/(r)_(1  mm) = 1.5  mm/0.5  mm = 3

The rate constant for the 1 mm lumen is calculated from the rateconstant 0.46 sec⁻¹ for the 3 mm lumen and from the two factors forsurface to volume ratio and diffusion radius ratio:k for 1 mm=0.46 sec⁻¹×3×3=4.14 sec⁻¹

A similar calculation is made for the rate constant for the 0.8 mmlumen:k for 0.8 mm=0.46 sec⁻¹×1.5/0.4×1.5/0.4=6.47 sec⁻¹

In this one-dimensional model for transport in the axial x direction inthe lumen, radial transport effects are addressed by adjusting the rateconstant. If the differential equation for the mass balance were statedin cylindrical coordinates instead of Cartesian coordinates,two-dimensional transport in the axial and radial directions would berepresented in the solution, and no adjustment for lumen size would berequired in the rate constant. However, the differential equation fortransient two-dimensional transport with a reaction term has noanalytical solution and must be solved numerically. The sterilizercomputer 28 could be used to obtain an approximate solution to thetwo-dimensional model, but practical limits on the available on-boardmemory limit the preferred implementation of the model to theone-dimensional case.

The area scale for the second lumen material, polyethylene (PE), inTable 1 is established similarly for a limiting case in the STERRAD® 200Sterilizer. The rate constant is set at 0.33 sec⁻¹ for 1 mm×500 mmlumens to give an area of approximately 100 mg-sec/l. Longer lumens 1mm×700 mm with the same rate constant have an area less than 100mg-sec/l with biological results in the positive region. The rateconstant 0.33 sec⁻¹ for lumens with 1 mm diameter is corrected withfactors for the surface to volume ratio and diffusion radius ratio toobtain the rate constant 0.037 sec⁻¹ for 3 mm lumens. Area for 3 mm×1000mm polyethylene lumens is greater than 100 mg-sec/l and the biologicalresults are negative, while area for 3 mm×1500 mm lumens is about 100mg-sec/l with positive biological results. By increasing the injectiontime in Table 1 from 6.5 minutes to 20, 25 and 30 minutes, the area for3 mm×1500 mm lumens increases beyond the 100 mg-sec/l threshold and thebiological results are negative.

If the results in Table 1 are rearranged according to the magnitude ofarea under the concentration-time curve, an interesting pattern becomesapparent in Table 3. All lumens with area greater than or equal to 110mg-sec/l have only negative biological indicators. Lumens with area near100 mg-sec/l have either negative or some positive indicators, while alllumens with area less than 90 mg-sec/l have at least one positivebiological indicator. These results demonstrate that area under theconcentration-time curve from the model correlates well with efficacy ina variety of lumen sizes and materials. Therefore, area may be usedduring the sterilization cycle as a tool in real time to accept or tocancel a sterilization cycle. The inputs to the model are readilyavailable with sterilizer software. Process variables of pressure,concentration and time are monitored during the sterilization cycle,while the temperature, dimensions and composition of the mostrestrictive load element could be entered for each cycle by theoperator. Devices 18 could be identified with a code, especially amachine readable code such as a bar code, which would either contain thephysical parameters itself or relate to a set of parameters storedwithin the control system 26. The temperature of the lumen material,rather than being assumed as room temperature and entered, could bemeasured during the cycle.

TABLE 3 Results for the STERRAD ® 200 Sterilizer Arranged by Area underthe Curve Temp. Mid-Lumen Frac- ° C. Injec- H₂O₂ Con- tion Indi- Lumen(lumen tion centration vs. Posi- cator mm diam. × materi- Time, −k, Time· Area, tive Results mm length al) min. sec⁻¹ mg · sec./1 BIs Zone   3 ×400 SS 30 6.5 0.46 168, 156, 157 0/72 Nega-   1 × 125 SS 30 6.5 4.14139, 143, 149 0/36 tive 0.8 × 100 SS 30 6.5 6.47 133, 137, 140, 0/48 136  3 × 1000 PE 30 6.5 0.037 262, 261, 245 0/36   3 × 1500 PE 30 20, 0.037179, 188, 205 0/36 25, 30   3 × 500 SS 30 6.5 0.46 101, 93, 91 0/96Mixed   3 × 400 SS 30 2 0.46 106, 104, 108 0/72 Positive   3 × 400 SS 301 0.46 97, 100, 108 4/72 and   1 × 500 PE 30 6.5 0.33 104, 107, 108 0/36Nega-   3 × 1500 PE 30 6.5 0.037 99, 102, 97 1/36 tive   3 × 400 SS  56.5 1.41 53, 50, 50 1/72 Positive 0.8 × 150 SS 30 6.5 6.47 43, 44 2/24  1 × 700 PE 30 6.5 0.33 34 1/12

A special feature of this model is demonstrated in Table 3 for bothpolyethylene and stainless steel lumens. In the 3 mm×1500 mmpolyethylene lumen an injection time of 6.5 minutes produces an area atthe center of the lumen of about 100 mg-sec/l with biological results inthe mixed zone. If this area were calculated during a sterilizationcycle, the software could elect to increase the hydrogen peroxideexposure time (injection and/or diffusion step times) until the areaincreased to a value greater than or equal to 110 mg-sec/l to achieveefficacy. This approach is demonstrated in Table 3 in the cycles with 3mm×1500 mm lumens for injection times of 20, 25 and 30 minutes. Forthese three cases, the areas are greater than or equal to 110 mg-sec/land efficacy is achieved in all cases. A similar result is observed in 3mm×400 mm stainless steel lumens. Injection times of 1 and 2 minutescorrespond to areas near 100 mg-sec/l with biological indicators in themixed zone, while increasing the injection time to 6.5 minutes producesareas greater than or equal to 110 mg-sec/l and only negative biologicalindicators. Employing area under the concentration-time curve in thesterilization cycle at a hydrogen peroxide transport-restricted regionof the load, such as at the center 32 of the lumen 20, would improvesterilizer performance by reducing the number of canceled cycles. Itwould also offer an additional measurement for parametric release of theload to complement temperature, pressure and concentration in thechamber.

The studies in Table 1 were conducted at the minimum injection quantityof hydrogen peroxide necessary to achieve efficacy, but in practice thehydrogen peroxide solution injected into the sterilizer may be a greaterquantity due to a larger injection volume or a greater initial solutionconcentration. In these cases, the area under the concentration-timecurve would reach the threshold of 110 mg-sec/l at a shorter injectiontime, so the entire cycle time could be shortened to offer a benefit ofquicker turn-around time for the operator.

If a load at a lower initial temperature were placed into thesterilizer, the pre-heating time of the cycle could be increased withplasma or convection heating to warm the load before injection to allowthe area under the concentration-time curve to reach the threshold of110 mg-sec/l. In this case, an initially cold load would not result in acycle cancellation, so process performance would be enhanced by reducingthe frequency of cycle cancellations.

Hydrogen peroxide exposure time, hydrogen peroxide injection quantityand load temperature before injection may all be used to increase thearea under the concentration-time curve to the threshold of 110mg-sec/l. As a result, process performance would be improved by reducingthe frequency of cycle cancellation or by offering a shorter cycle timeto the operator.

Although the foregoing description of the preferred embodiments of thepresent invention has shown, described and pointed out the fundamentalnovel features of the invention, it will be understood that variousomissions, substitutions, and changes in the form of the detail of theapparatus and method as illustrated as well as the uses thereof, may bemade by those skilled in the art, without departing from the spirit ofthe present invention. Consequently, the scope of the present inventionshould not be limited to the foregoing discussions, but should bedefined by the appended claims.

1. A method for assessing a sterilization of a lumen of a device in avapor phase hydrogen peroxide sterilization process, the methodcomprising the steps of: a) measuring concentration of hydrogen peroxidevapor exterior of the lumen; b) calculating at least once aconcentration of hydrogen peroxide at a selected location within thelumen based upon time of exposure, concentration of hydrogen peroxideexterior of the lumen and the physical characteristics of the lumen,wherein the physical characteristics of the lumen comprise: diameter ofthe lumen, length of the lumen to the selected location, type ofmaterial forming the lumen and temperature of the material forming thelumen; c) indicating a parameter relevant to said sterilization of saidlumen based upon said concentration of said hydrogen peroxide at theselected location; and wherein the concentration of hydrogen peroxide atthe selected location is calculated based upon the followingrelationship:${\left. \left. {C_{p} = {C_{o} + {\left( {4k\;{c_{o}/\pi}} \right)\left\{ {\sum\limits^{\;}{\left\lbrack {\sin\left( {n\;\pi\;{x/L}} \right)} \right){\left( {\left( {\exp\left( {t\left( {k - {D\left( {n\;{\pi/L}} \right)}^{2}} \right)} \right)} \right) - 1} \right)/{n\left( {k - {D\left( {n\;{\pi/L}} \right)}^{2}} \right)}}}} \right)}}} \right\rbrack \right\} - {\left( {4c_{o}{\exp({kt})}} \right){\left\{ {\sum\left\lbrack {\left( {\sin\left( {n\;\pi\;{x/L}} \right)} \right)\left( {\exp\left( {- {{Dt}\left( {n\;{\pi/L}} \right)}^{2}} \right)} \right)} \right\rbrack} \right\}/\pi}}};$where: c_(p) represents the concentration of hydrogen peroxide at theselected location; c_(o) represents the concentration exterior of thelumen; k represents a rate constant for losses of hydrogen peroxide; Lrepresents the length of the lumen; D represents the diffusioncoefficient for hydrogen peroxide vapor; x represents the distance intothe lumen to the selected location from exterior of the lumen nrepresents odd integer counters 1, 3, 5, . . . ; and t represents thetime from when hydrogen peroxide vapor first is introduced exterior ofthe lumen.
 2. A method according to claim 1 wherein the step ofindicating comprises displaying to a user said parameter relevant to thesterilization of the lumen.
 3. A method according to claim 1 wherein theparameter relevant to the sterilization of the lumen comprises theconcentration of said hydrogen peroxide at the selected location.
 4. Amethod according to claim 1 wherein the parameter relevant to thesterilization of the lumen is success or failure of the sterilization ofthe lumen.
 5. A method according to claim 1 wherein k is determined atleast in part based upon a material forming the lumen, the diameter ofthe lumen and the temperature of the material forming the lumen.
 6. Amethod for controlling sterilization of a lumen of a device in a vaporphase hydrogen peroxide sterilization process, the method comprising thesteps of: measuring a concentration of hydrogen peroxide vapor exteriorof the lumen; calculating at least once a concentration of hydrogenperoxide at a selected location within the lumen based upon processparameters of the sterilization process and physical characteristics ofthe lumen, wherein the process parameters include the concentration ofhydrogen peroxide exterior of the lumen and wherein the physicalcharacteristics of the lumen comprise: diameter of the lumen, length ofthe lumen to the selected location, type of material forming the lumenand temperature of the material forming the lumen; adjusting a parameterof the sterilization process based upon the at least one calculatedconcentration of hydrogen peroxide at the selected location; and whereinthe concentration of hydrogen peroxide at the selected location iscalculated based upon the following relationship:${\left. \left. {C_{p} = {C_{o} + {\left( {4k\;{c_{o}/\pi}} \right)\left\{ {\sum\limits^{\;}{\left\lbrack {\sin\left( {n\;\pi\;{x/L}} \right)} \right){\left( {\left( {\exp\left( {t\left( {k - {D\left( {n\;{\pi/L}} \right)}^{2}} \right)} \right)} \right) - 1} \right)/{n\left( {k - {D\left( {n\;{\pi/L}} \right)}^{2}} \right)}}}} \right)}}} \right\rbrack \right\} - {\left( {4c_{o}{\exp({kt})}} \right){\left\{ {\sum\left\lbrack {\left( {\sin\left( {n\;\pi\;{x/L}} \right)} \right)\left( {\exp\left( {- {{Dt}\left( {n\;{\pi/L}} \right)}^{2}} \right)} \right)} \right\rbrack} \right\}/\pi}}};$where: c_(p) represents the concentration of hydrogen peroxide at theselected location; c_(o) represents the concentration exterior of thelumen; k represents a rate constant for losses of hydrogen peroxide; Lrepresents the length of the lumen; D represents the diffusioncoefficient for hydrogen peroxide vapor; x represents the distance intothe lumen to the selected location from exterior of the lumen nrepresents odd integer counters 1, 3, 5, . . . ; and t represents thetime from when hydrogen peroxide vapor first is introduced exterior ofthe lumen.
 7. A method according to claim 6 wherein the processparameters used in the step of calculating at least once a concentrationof hydrogen peroxide vapor at the selected location within the lumencomprise: pressure exterior of the lumen, the concentration of peroxideexterior of the lumen and time.
 8. A method according to claim 6 whereinthe step of adjusting a parameter of the sterilization process comprisesadjusting a time of exposure of the device to the vapor phase hydrogenperoxide.
 9. A method according to claim 6 wherein the step of adjustinga parameter of the sterilization process comprises adjusting theconcentration of the hydrogen peroxide exterior of the lumen.
 10. Amethod according to claim 6 and further comprising modifying a parameterof the sterilization process upon achieving a preselected value ofhydrogen peroxide at the selected location.
 11. A method according toclaim 6 and further comprising the step of calculating an integratedtime and concentration exposure of the selected location to the hydrogenperoxide.
 12. A method according to claim 11 and further comprising thestep of modifying a parameter of the sterilization process uponachieving a preselected value of the integrated time and concentrationexposure at the selected location.
 13. A method according to claim 6wherein k is determined at least in part based upon a material formingthe lumen, the diameter of the lumen and the temperature of the materialforming the lumen.